4. Determine the lateral and total surface area of the rectangular pyramid. 6 cm 8 cm 6 cm Lateral Surface Area Total Surface Area 6.5 cm​

The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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The value of x in the line intersection is 60.

When line intersect, angle relationships are formed such as linear angles, vertical angles etc.

Therefore, lets use the angle relationship to find the value of x in the line intersection.

Hence,

2x - 10 + 2x + 40 + 90 = 360(sum of angles in a point)

2x - 10 + 2x + 130 = 360

4x + 120 = 360

4x = 360 - 120

4x = 240

divide both sides by 4

x = 240 / 4

x = 60

Therefore,

x = 60

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The area of triangle ABC is approximately 231.89 square inches.

To solve this problem, we'll use the properties of a triangle and trigonometric functions.

Let's go step by step.

Part A: Determine m ∠A.

To find the measure of angle A, we can use the Law of Cosines.

The Law of Cosines states that for a triangle with sides of lengths a, b, and c, and angle A opposite side a, we have the formula:

c² = a² + b² - 2ab × cos(A)

In this case, c = 60 inches, a = 60 inches, and b = 60√2 inches.

Plugging in these values into the Law of Cosines equation, we get:

(60)² = (60)² + (60√2)² - 2(60)(60√2) × cos(A)

Simplifying:

3600 = 3600 + 7200 - 7200√2 × cos(A)

Now, let's solve for cos(A):

7200√2 × cos(A) = 7200

cos(A) = 7200 / (7200√2)

cos(A) = 1 / √2

cos(A) = √2 / 2

To determine the angle A, we need to find the inverse cosine of (√2 / 2), which is 45 degrees.

Therefore, m ∠A is 45 degrees.

Part B: Explain how to use the unit circle to find the exact values of all six trigonometric functions evaluated at A.

To find the values of the trigonometric functions at angle A, which is 45 degrees or π/4 radians, we can use the unit circle.

The unit circle is a circle with a radius of 1 unit, centered at the origin (0, 0) in a coordinate plane.

At angle A = 45 degrees or π/4 radians, the coordinates of the point on the unit circle are (√2/2, √2/2).

Using these coordinates, we can find the exact values of the trigonometric functions as follows:

sin(A) = y-coordinate = √2/2

cos(A) = x-coordinate = √2/2

tan(A) = sin(A) / cos(A) = (√2/2) / (√2/2) = 1

csc(A) = 1 / sin(A) = 1 / (√2/2) = √2

sec(A) = 1 / cos(A) = 1 / (√2/2) = √2

cot(A) = 1 / tan(A) = 1 / 1 = 1

Part C: Calculate the area of triangle ABC.

To calculate the area of triangle ABC, we can use Heron's formula, which is based on the lengths of the triangle's sides.

Heron's formula states that for a triangle with side lengths a, b, and c, the area (A) can be calculated as:

A = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, a = 60 inches, b = 60√2 inches, and c = 60 inches.

Calculating the semiperimeter:

s = (60 + 60√2 + 60) / 2

s = (120 + 60√2) / 2

s = 60 + 30√2

Now, we can calculate the area using Heron's formula:

A = √((60 + 30√2)((60 + 30√2) - 60)((60 + 30√2) - (60√2))((60 + 30√2) - 60))

Simplifying:

A = √((60 + 30√2)(60)(30√2)(30))

A = √(1800(30√2))

A = √(54,000√2)

A = 231.89 square inches (rounded to the nearest hundredth)

Therefore, the area of triangle ABC is approximately 231.89 square inches.

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Kelvin and Fiona had a total of 200 + 200 = 400 postcards left together. Let's assume that Kelvin had x postcards initially. Fiona would then have (600 - x) postcards since they had a total of 600 numbers postcards altogether.

After Kelvin donated 2/7 of his postcards, he would have (1 - 2/7)x = (5/7)x postcards left.

Fiona gave away 120 postcards, so she would have (600 - x - 120) = (480 - x) postcards left.

According to the problem, both Kelvin and Fiona had the same number of postcards left. Therefore, we can set up an equation:

(5/7)x = 480 - x

Multiplying both sides of the equation by 7 to eliminate the fraction, we get:

5x = 3360 - 7x

Combining like terms, we have:

12x = 3360

Dividing both sides by 12, we find:

x = 280

So, Kelvin initially had 280 postcards, and Fiona had (600 - 280) = 320 postcards.

After Kelvin donated 2/7 of his postcards, he had (5/7) * 280 = 200 postcards left.

After Fiona gave away 120 postcards, she had (320 - 120) = 200 postcards left.

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The input value which produces the same output values for the two functions in the graph is x=1

To determine which input value produces the same output value for two functions on a graph

we need to find the x-coordinate(s) where the two functions intersect or have the same y-coordinate.

x=1 is the input value which produces the same output values for the two functions in the graph

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Answer:

∠CDF = 48°

Step-by-step explanation:

∠CDE = ∠EDF + ∠CDF

Given that,

∠CDE = 114°

∠EDF = 66°

So, to find the value of ∠CDF, you have to subtract the value of ∠EDF from ∠CDE.

∠CDF = ∠CDE - ∠EDF

∠CDF = 114 - 66

∠CDF = 48°

Answer:

5 seconds

Step-by-step explanation:

20-15= 5 seconds

Six over ten >_three over four__> one over two

D three over four.

To determine the fraction that goes in the blank, we need to compare the fractions six over ten and one over two.

To compare fractions, we can either find a common denominator or convert them into decimal form.

Let's go with the decimal approach.

To convert six over ten into a decimal, we divide 6 by 10, which equals 0.6. Similarly, for one over two, dividing 1 by 2 gives us 0.5.

Now, we can see that 0.6 is greater than 0.5.

Since six over ten is greater than one over two, we need to find a fraction that is greater than 0.6 but less than 0.5.

Among the given options, the only fraction that fits this criterion is three over four (option D).

To confirm this, let's convert three over four into a decimal.

Dividing 3 by 4 gives us 0.75, which is greater than 0.6 and less than 0.5.

Therefore, we can conclude that the correct fraction to fill in the blank is three over four (D).

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Answer:

Step-by-step explanation: -3 is on the x-axis so you have to put your point at the left ,and 0 is the Y-axis. When is is zero that means that x stays on its line.

E is the correct answer.

Candidate A would win the election using the plurality method.

According to the given preference schedule, the number of votes and the corresponding preferences are as follows:

Candidate A: 15 (1st preference: A, 2nd preference: D, 3rd preference: B)

Candidate B: 11 (1st preference: D, 2nd preference: C, 3rd preference: A)

Candidate C: 9 (1st preference: B, 2nd preference: C, 3rd preference: A)

Candidate D: 6 (1st preference: C, 2nd preference: D, 3rd preference: A)

Candidate E: 2 (1st preference: C, 2nd preference: D)

To determine the winner using the plurality method, we look at the candidate with the highest number of first preference votes.

In this case, Candidate A has 15 first preference votes, which is the highest.

Therefore, Candidate A would win the election using the plurality method.

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The number of quarters he originally think we're in his pocket is 33.

We are given that;

More quarters she had= 2

Total= $8.75

Now,

Let’s name that number x.

We can translate the table into an equation by equating the total value of the quarters to $8.75:

0.25(x + 2) = 8.75

To solve this equation by simplifying and isolating x:

0.25x + 0.5 = 8.75 0.25x = 8.25 x = 33

The answer by plugging it back into the equation:

0.25(33 + 2) = 8.75 0.25(35) = 8.75 8.75 = 8.75

This makes sense, so we have the correct answer. 7.

Therefore, by algebra the answer will be 33.

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The total police officers there altogether given the percentage of police officers who have ride-alongs with teenagers is 430.

Percentage of police officers who have ride-alongs with teenagers = 60%

Number of Percentage of police officers who have ride-alongs = 258

Total police officers = x

So,

(Percentage of police officers who have ride-alongs with teenagers) of (Total police officers) = (Number of Percentage of police officers who have ride-alongs)

60% of x = 258

0.6 × x = 258

0.6x = 258

divide both sides by 0.6

x = 258/0.6

x = 430

Ultimately, there are 430 police officers altogether.

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Answer:

The word or phrase that describes the probability that Arianna will roll a number between 1 and 6 (including 1 and 6) is "certain." The reason for this is that a standard six-sided die always has a number between 1 and 6 on each face, and if the die is fair and unbiased, then the probability of rolling a number between 1 and 6 is 1, or 100%. Therefore, option (b) "certain" is the correct choice.

Answer:

Step-by-step explanation:

To find the probability of drawing a purple and yellow marble without replacement, we need to determine the number of favorable outcomes (purple and yellow marbles) and the total number of possible outcomes.

Step 1: Determine the number of purple marbles:

The given information states that there are 6 purple marbles.

Step 2: Determine the number of yellow marbles:

The given information states that there are 3 yellow marbles.

Step 3: Determine the total number of marbles:

The given information states that there are 25 marbles in total.

Step 4: Calculate the probability of drawing a purple and yellow marble:

When drawing without replacement, the probability of two events occurring is the product of their individual probabilities.

The probability of drawing a purple marble is: 6 purple marbles / 25 total marbles = 6/25.

After drawing a purple marble, the total number of marbles remaining is 24 (since one purple marble is already drawn).

The probability of drawing a yellow marble from the remaining marbles is: 3 yellow marbles / 24 remaining marbles = 3/24.

To find the probability of both events occurring (drawing a purple and yellow marble), we multiply their individual probabilities:

Probability of drawing a purple and yellow marble = (6/25) * (3/24) = 18/600 = 3/100.

Therefore, the probability of drawing a purple and yellow marble without replacement is 3/100.

Answer:

The distance formula is:

[tex]d = \sqrt{(x_2 - x_1)^2+ (y_2 - y_1)^2}[/tex]

Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]are the coordinates of the two points.

(-2, 5) & (0, -4):

[tex]d = \sqrt{(0 - (-2))^2+ ((-4) - 5)^2}=\sqrt{85}[/tex]

So the distance between (-2, 5) and (0, -4) is [tex]\sqrt{85}[/tex].

(0,-4) & (5, 3):

[tex]d = \sqrt{(5 - 0)^2+ ((3) - (-4))^2}=\sqrt{74}[/tex]

So the distance between (0,-4) and (5, 3) is [tex]\sqrt{74}[/tex]

(5, 3) & (-2, 5):

[tex]d = \sqrt{(5 - (-2))^2 + ((3) - 5)^2}=\sqrt{53}[/tex]

So the distance between (5, 3) and (-2, 5) is [tex]\sqrt{53}[/tex].

Answer:

[tex]\sqrt{85}\approx 9.23 \; \sf units\;(3\;s.f.)[/tex]

[tex]\sqrt{74}\approx 8.60\; \sf units\; (3\;s.f.)[/tex]

[tex]\sqrt{53}\approx 7.28\; \sf units \;(3\;s.f.)[/tex]

Step-by-step explanation:

The distance formula is a mathematical equation used to calculate the distance between two points in a coordinate system.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

To find the distance between each set of two points, substitute the coordinates of the points into the distance formula and solve for d.

The distance between points (-2, 5) and (0, -4) is:

[tex]\begin{aligned}d&=\sqrt{(0-(-2))^2+(-4-5)^2}\\&=\sqrt{(2)^2+(-9)^2}\\&=\sqrt{4+81}\\&=\sqrt{85}\\&\approx 9.23 \; \sf units\;(3\;s.f.)\end{aligned}[/tex]

The distance between points (0, -4) and (5, 3) is:

[tex]\begin{aligned}d&=\sqrt{(5-0)^2+(3-(-4))^2}\\&=\sqrt{(5)^2+(7)^2}\\&=\sqrt{25+49}\\&=\sqrt{74}\\&\approx 8.60\; \sf units\; (3\;s.f.)\end{aligned}[/tex]

The distance between points (5, 3) and (-2, 5) is:

[tex]\begin{aligned}d&=\sqrt{(-2-5)^2+(5-3)^2}\\&=\sqrt{(-7)^2+(2)^2}\\&=\sqrt{49+4}\\&=\sqrt{53}\\&\approx 7.28\; \sf units \;(3\;s.f.)\end{aligned}[/tex]

The statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true.

Given, two functions  y = -2f(x) = 1/x

To determine whether the statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true or false, we need to find the value of Y for both functions when x = -2.

Substituting x = -2 in the functions we get:I would ask y = -2(-2) = 4f(-2) = 1/(-2) = -1/2Therefore, the Y value of the function I would ask is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2. Hence, the given statement is true.

Therefore, the statement "the Y value of function I would ask equals -2 is greater than the Y value function be when I ask equals negative to the Y value function a 1X equals -2 is less than the Y value a function be one x was -2" is true.

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844,758,200,030 will be rounded to 845 billion (845,000,000,000).

The rounding digit is 5.

Estimation a is a method used for calculating the approximate value of a quantity (just to get a 'rough answer')

In estimation 1, 2,3, and 4 are rounded down while 5, 6, 7, 8 and 9 are rounded up.

To round 844,758,200,030 to the nearest billion, we look at the digit in the hundred millionths place, which is 7.

Since 7 is greater than or equal to 5, we round 844,758,200,030 up to 845,000,000,000. The rounding digit is therefore 5.

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Answer:

The length of the third side is 1 unit.

Step-by-step explanation:

Because this is a right triangle, we can use the Pythagorean theorem to solve for the hypotenuse.
Pythagorean theorem: a² + b² = c², where variables a and b are the legs of the triangle and c is the hypotenuse

We are going to let a = (12/13) and b = (5/13), though the order does not particularly matter in this case. We are going to plug and play with the theorem, and then simplify as we go.

[tex](\frac{12}{13})^{2} + (\frac{5}{13})^{2} = c^{2}\\\\\frac{144}{169} + \frac{25}{169} = c^{2}\\\\\frac{144 + 25}{169} = c^{2}\\ \\ \frac{169}{169} = c^{2}\\\\1 = c^{2}\\\\\sqrt{1} = \sqrt{c^{2}} \\\\c = 1[/tex]

The amplitude and the period of the function f(x) = cos(5θ) are 1 and 2π/5

Here, we have,

to determine the amplitude and period of the function

From the question, we have the following parameters that can be used in our computation:

f(x) = cos(5θ)

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

Amplitude = A

Period = 2π/B

So, we have

A = 1

Period = 2π/5

Evaluate

A = 1

Period = 2π/5

Hence, the amplitude is 1 and the period is 2π/5

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complete question:

100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!

Answer:

Solution is in the attached photo.

Step-by-step explanation:

This question tests on the concept on deriving equations and substitution of values.

The pounds of seafood at the boil was 10 37/40 pounds

A fraction is defined as the part of a whole number, a whole element or a whole variable.

The types of fractions are listed as;

From the information given, we have that;

5 4/5 + 4 1/2 + 5/8, all in pounds

convert the mixed fraction to improper fractions, we have;

29/5 + 9/2 + 5/8

Find the lowest common factor, we have;

232 + 180 + 25  /40

Add the values

437/40

Divide the values

10 37/40 pounds

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√x+3 is an increasing function, the minimum value is L4 and the maximum value is R4.

Since we are given 4 subintervals, the width of each subinterval is:

Δx = (b - a) / n = (1 - (-1)) / 4 = 1/2

where a = -1 and b = 1 are the endpoints of the interval.

Now, L4 = f(-1)Δx + f(-1/2)Δx + f(0)Δx + f(1/2)Δx

= √2/Δx + √3/Δx + √3/Δx + √4/Δx

= (2√2 + 2√3 + 2√4) / Δx

= 10(2√2 + 2√3 + 2√4)

and, the right endpoint Riemann sum,

R4 = f(-1/2)Δx + f(0)Δx + f(1/2)Δx + f(1)Δx

= √3/Δx + √3/Δx + √4/Δx + √5/Δx

= (2√3 + 2√4 + 2√5) / Δx

= 4(√3 + 2√4 + √5)

Since √x+3 is an increasing function, the minimum value is L4 and the maximum value is R4.

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Answer:

B. 11

Step-by-step explanation:

√380.13/pi = 10.99, Round: 11

The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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As per the given details, the area of the trapezoid is 112.5 cm².

The lengths of the two parallel sides and the height are required to determine the area of a trapezium. In this instance, the metrics are as follows:

Base 1 = 9 cm

Base 2 = 6 cm

Height = 15 cm

Area = (Base 1 + Base 2) * Height / 2

Area = (9 + 6) x 15 / 2

Area = 15 x 15 / 2

Area = 225 / 2

Area = 112.5 cm²

Thus, the answer is 112.5 cm².

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The values of the different parameters of the shapes given would be =

5.) = 78.5 in²

6.) = 54cm²

7.) = 50.24 ft²

8.) = 108yd³

10.) = 320mm³

11.)=847.8m³

12.)=366.3ft³

13.)=1004.8in

14.)=113.04in³

For question 5.)

Area of base of cylinder = πr²

radius = 5 in

area = 3.14×5×5 = 78.5 in²

For question 6.)

Area of base of rectangular pyramid = l×w

length = 6 cm

width = 9 cm

Area = 6×9 = 54cm²

For question 7.)

Area of the base of a cone = πr²

radius = 4 ft

area = 3.14×4×4 = 50.24 ft²

For question 8.)

Volume of a square pyramid =1/3 a²h

a = 6 yd

h = 9yd

volume = 1/3× 6×6× 9

= 108yd³

For question 10.)

Volume of the rectangular pyramid;

= 1/3×l×W×h

width= 12mm

height = 8 mm

length = 10

Volume = 1/3× 12×8×10 = 320mm³

For question 11.)

Volume of a cone= ⅓πr²h

height = 10m

radius = 9m

Vol = ⅓×3.14×9×9×10

= 847.8m³

For question 12.)

Volume of cone = ⅓πr²h

height = 14ft

radius = 5ft

Volume = 1/3×3.14×5×5×14

= 366.3ft³

For question 13.)

Volume of cone = ⅓πr²h

height = 15in

radius = 16/2 = 8in

Volume = 1/3× 3.14× 8×8×15

= 1004.8in

For question 14.)

Volume of cone = ⅓πr²h

height = 12in

radius = 3in

volume = 1/3×3.14×3×3×12

= 113.04in³

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The mean monthly rainfall is 3.245 inches.

For a set of N numbers {x₁, x₂, ...}, the mean of these N numbers is:

M = {x₁ + x₂ + ...}/N

Here we want to find the mean of the rainfall in inches, then we just need to add the 12 values in the table and then divide by 12, we will get:

M = (2.22+1.51+1.86+2.06+3.48+4.57+ 3.27 + 5.40 + 5.45 + 4.34+2.64+ 2.14)/12

M = 3.245

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Answer:

Step-by-step explanation:

Answer:

50.8

Step-by-step explanation:

name me brainliest please.

The statement you provided refers to a concept known as Russell's paradox in set theory.

The paradox arises when we consider the set of all sets that do not contain themselves as elements. If we assume such a set exists, we can define a paradoxical set, often denoted as R, which contains all sets that do not contain themselves.

The statement you provided is suggesting that the paradox arises from the concept of the set of all sets, rather than from the concept of comprehension itself.

The , in set theory, refers to the idea of defining a set by specifying a property or condition that its elements must satisfy. The paradox does not arise from the idea of defining sets in this way but rather from the specific concept of the set of all sets.

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Explanation:

Each cube has side length 1/2. The volume of each smaller cube is (1/2)^3 = 1/8 cubic units.

The box holds 2 layers and 15 cubes per layer. There are 2*15 = 30 cubes total. The total volume of all 30 cubes is 30*(1/8) = 30/8 = 15/4 = 3.75 cubic units, which also represents the volume of the box.